Question $1.$ A vessel contains $5\mathrm{.}0f{t}^3$ of water at $40F$ and atmospheric pressure. If the water is heated to $80F,$ what will be the percentage change in its volume? What weight of water must be removed to maintain the volume at its original value? Use Figure $2\mathrm{.}1$

Question $2.$ If an NG $($natural gas$)$ consists of $20\%$ nitrogen and $80\%$ methane by volume, at $14\mathrm{.}7$ psia and $20C,$ what are $($a$)$ the specific weight and partial pressure of the methane and $($b$)$ the specific weight of the mixture? Using Table A$.5$ & DALTON'S LAW

Question $3.$ Prove the following equation $($Eq$.1\mathrm{.}12)$ using the state and process equations for the ideal gas and explain the physical meaning of Eq$.1\mathrm{.}12$

$\frac{T_2}{T_1}=(\frac{v_1}{v_2}{)}^{n-1}=(\frac{{}_2}{{}_1}{)}^{n-1}=(\frac{p_2}{p_1}{)}^{\frac{n-1}{n}}$